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Ben is 3 times as old as Daniel and is also 4 years older than Daniel.
How old is Ben?

Ben is \(3\) times as old as Daniel and is also \(4\) years older than Daniel. $\newline$ How old is Ben?

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Solve a system of equations using any method: word problems

Full solution

Q. Ben is \(3\) times as old as Daniel and is also \(4\) years older than Daniel.

\newline

How old is Ben?

Denoting Ben and Daniel's ages: Let's denote Ben's age as $B$ and Daniel's age as $D$ . According to the problem, Ben is $3$ times as old as Daniel. We can write this as an equation: $\newline$ $B = 3D$
Equation $1$ : Ben is $3$ times as old as Daniel: The problem also states that Ben is $4$ years older than Daniel. We can write this as another equation: $\newline$ $B = D + 4$
Equation $2$ : Ben is $4$ years older than Daniel: Now we have a system of two equations with two variables: $\newline$ $1$ ) $B = 3D$ $\newline$ $2$ ) $B = D + 4$ $\newline$ We can set these two equations equal to each other since they both equal $B$ . $\newline$ $3D = D + 4$
System of equations: To find the value of $D$ , we will subtract $D$ from both sides of the equation: $\newline$ $3D - D = D + 4 - D$ $\newline$ $2D = 4$
Setting equations equal to each other: Now we divide both sides by $2$ to solve for D: $\newline$ $\frac{2D}{2} = \frac{4}{2}$ $\newline$ $D = 2$
Simplifying the equation: Now that we have Daniel's age, we can find Ben's age by substituting $D$ back into one of the original equations. We'll use the first equation $B = 3D$ : $\newline$ $B = 3 \times 2$ $\newline$ $B = 6$

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